In this article, we will discuss creating matrices in Mathematica.

## Table of Contents

### Matrices in Mathematica

A matrix is an array of numbers arranged in rows and columns. In Mathematica, matrices are expressed as a list of rows, each of which is a list itself. It means a matrix is a list of lists. If a matrix has $n$ rows and $m$ columns then we call it an $n$ by $m$ matrix. The value(s) in the ith row and jth column is called the $i,j$ entry.

In Mathematica, matrices can be entered with the **{ }** notation, constructed from a formula, or imported from a data file. There are also commands for creating diagonal matrices, constant matrices, and other special matrix types.

### Creating Matrices in Mathematica

- Create a matrix using { } notation

mat={{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}

but the output will not be in matrix form, to get in matrix form use commands like

mat//MatrixForm - Creating matrix using Table command

mat1=Table[b{row, column},

{row, 1, 4, 1}, {column, 1, 2, 1}]

];

MatrixForm[mat1] - Creating symbolic matrices such as

mat2=Table[x^{i}+x^{j }, {i, 1, 4}, {j, 1, 3}]

mat2//MatrixForm - Creating a diagonal matrix with nonzero entries at its diagonal

DiagonalMatrix[{1, 2, 3, r}]//MatrixForm - Creating a matrix with the same entries i.e. a constant matrix

ConstantArray[3, {2, 4}]//MatrixForm - Creating an identity matrix of order $n\times n$
IdentityMatrix[4]

### Matrix Operations in Mathematica

In Mathematica, matrix operations can be performed on both numeric and symbolic matrices.

- To find the determinant of a matrix

Det[mat] - To find the transpose of a matrix

Transpose[mat] - To find the inverse of a matrix for a linear system

Inverse[mat] - To find the Trace of a matrix i.e. sum of diagonal elements in a matrix

Tr[mat] - To find the Eigenvalues of a matrix

Eigenvalues[mat] - To find the Eigenvector of a matrix

Eigenvector[mat] - To find both Eigenvalues and Eigenvectors together

Eigensystem[mat]

Note that +, *, and ^ operators all automatically work element-wise.

### Displaying Matrix and its Elements

- mat[[1]] displays the first row of a matrix where mat is a matrix created above
- mat[[1, 2]] displays the element from the first row and second column, i.e. m12 element of the matrix
- mat[[All, 2]] displays the 2nd column of matrix

### Interactive Input (Menu)

- Go to
**Insert**>**Table/Matrix**>**New…** - Select
**Matrix (List of lists)**. - Define the number of rows and columns.
- Click
**OK**. - Use the provided interface to enter values in each cell.

### Predefined Matrices

Mathematica provides functions to generate specific types of matrices:

**IdentityMatrix:**Creates an identity matrix.**DiagonalMatrix:**Creates a diagonal matrix from a specified list.**HilbertMatrix:**Generates a Hilbert matrix.**VandermondeMatrix:**Creates a Vandermonde matrix.

### Importing from Files

- Use the
`Import`

function to read data from various file formats like CSV, TSV, or Excel spreadsheets and convert them into matrices.

**References**